The velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen a fundamental units, then the dimensions of length will be - Padhle.Online
Students' favourite free learning app with LIVE online classes, instant doubt resolution, unlimited practice for classes 6-12, personalized study app for Maths, Science, Social Studies, video e-learning, online tutorial, and more. Download Now!

The velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen a fundamental units, then the dimensions of length will be

 Given: Velocity of light=C

Acceleration due to gravity – g

Pressure -P

Let ‘L’ be the length.

Let’s assume, L = CxgyPz …eq i)

Now putting all the values in above equation, [M0L1T0] = [M0L1T−1]x [M0L1T−2]y [M1L−1T−2]z

⇒ [M0L1T0] = [MzLx+y−zT−x−2y−2z]

Applying the principle of homogeneity, Comparing the powers of M, z=0

Compare the powers of L, x+y−z=1 ( As z=0)

⇒ x + y =1

⇒ x = 1−y …eq ii)

Compare the powers of T, −x−2y−2z=0 ( As z=0)

⇒ −x−2y=0 …eq iii)

Put the value of eq ii) in above equation, we get ⇒ −(1−y)−2y = 0

⇒ y = −1

Putting the value of y in eq ii),

we get ⇒ x = 2

Now, put the values of x, y and z in eq i)

Therefore, the dimensions of length will be: L = C2g−1P0

⇒ L=C2/g

About the Author

Principal, Babu Daudayal SVM, Mathura

Post a Comment

Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.